3.E-MATHS (2B)DIFFERENTIA TIGNLCHein fom firt principles, the derivative with respet toof the followiny functions definal bya. 4= x+5x - 32. Diffeentiate the llawing(2-3)32-1where equation is3. A cuve f the foom y=au?t buthasteirning point P usith coordlinates (),2).). Calculate the values Gf a Ś b.of(). Aetermine whother P is a maximumor minimumpoin

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

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This questions has to do with marginal anyalysis in my price thoery economics class. We have to find the derivative of a function and find maximums and minimums. I know this question might seem simple, but I am just conceptually confused. If y = f(x) write down the FOC for a for a minimum is given by dy/dx=.
4.2: 3) Use linear approximation, i.e. the tangent line, to approximate 1/1.001as follows: Let f(x)=1/x and find the equation of the tangent line to f(x) at a "nice" point near 1.001. Then use this to approximate 1/1.001.
3.2 (Based on Question 3 in the picture attached) Using the first derivative method, the stability properties of E0, E1, and E2 , respectively, are as follows: A. None B. stable, unstable, stable C. stable, unstable, unstable D. unstable, stable, stable
A) Given that the graph of f(x) passes through the point (6,9) and that the slope of its tangent line at (x,f(x)) is 3x+3, what is f(2)? B) find the particular anti derivative that satisfies the following conditions: dy/dx= 3x+5/ sqrt3 of x ; y(1)=8 * it’s 3 square root of x the 3 isn’t in front it’s in the V of the squareroot*
2. The functions u+2v=x^2-y^2 and 2u-v=2xy^2 are given. Find the derivative of d^2x/du^2.
The equation sin(πxy/3)+x=3y implicitly defines y as a single function of x at (and near) the point (3,1). Use the linearization of this implicitly defined function at (3,1) to approximate the value of y when x=3.14. Round your answer to three decimal places.
Find the derivative of the function. 1.G(y) = (y − 1)4 / (y2 + 2y)7 a. G'(y) = ? 2.Find y' and y''. a. y = eαx sin(βx) 3. Find an equation of the tangent line to the curve y = 6/(1 + e−x) at the point (0, 3). 4.If F(x) = f(g(x)), where f(−5) = 6, f '(−5) = 3, f '(2) = 2, g(2) = −5, and g'(2) = 8, find F '(2). F '(2) = ? 5. For what values of r does the function y = erx satisfy the differential equation y'' − 8y' + 2y = 0? (Enter your answers as a comma-separated list.) a. r = ?
6) If y = f(x) has slope −4 at x = 3, and y value 5 at x = 3, a) write the formula for the tangent line to f(x) at x=3: b) estimate f(3.02) from the tangent line: c) If f is known to be concave up (S), is f(3.02) bigger than or smaller than your answer in b)?
4.2(2) With the equation (shown in the picture) Determines each of the derivatives below in the (a, b, c, d)
Consider a function y =f(t) with domain (0. 1, 4. 2).Use the graph of the derivative function, y=f'(t) ,given below to write down the t -value of the local maximum of f. If the function has no local maximum, explain why not
3. The curve y =ax2 +bx +c passes through the point (2, 4) and is tangent to the line y = x + 1 at (0, 1). Determine values for a, b, and c. Gauss sits at the point (-b –c, 4a).
Suppose u and y are functions of x that are differentiable atx = 0 and that u(0) = 5, u(0) = -3, y(0) = -1, y(0) = 2.Find the values of the following derivatives at x = 0.

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